Locking-free finite elements  for the Reissner-Mindlin plate

Falk, Richard S.; Tu, Tong

doi:10.1090/s0025-5718-99-01165-5

Cited by 44 publications

(27 citation statements)

References 36 publications

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“…We consider the following formulation of the Reissner-Mindlin plate with clamped boundary condition [1,3,12]. The Reissner-Mindlin plate problem C5 is to find the transverse displacement of the mid-plane section Ω of the plate denoted by u and the rotation φ of the transverse normal vector.…”

Section: A Mixed Formulation For Reissner-mindlin Platesmentioning

confidence: 99%

A new MITC finite element method for Reissner--Mindlin plate problem based on a biorthogonal system

Lamichhane¹,

Meylan²

2017

ANZIAMJ

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Section: A Mixed Formulation For Reissner-mindlin Platesmentioning

confidence: 99%

A new MITC finite element method for Reissner--Mindlin plate problem based on a biorthogonal system

Lamichhane¹,

Meylan²

2017

ANZIAMJ

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“…[η] ds (|e| := length of the edge e), (11) and κ e is a positive constant having the same physical dimension as C (for instance, for smooth C one could take κ e as |C| evaluated at the midpoint of e). Furthermore, R h : H 1 (T h ) → Γ h is a suitable 'reduction' operator, to be defined case by case.…”

Section: The Reissner-mindlin Problem and The Nonconforming Elementsmentioning

confidence: 99%

“…We point out that nowadays a wide choice of good elements are avalaible in the literature (see, for instance, [1]- [3], [5]- [7], [11]- [15], and the references therein). The aim of this Note is to discuss some finite element schemes recently proposed and studied in [6], [9], and [12].…”

Section: Introductionmentioning

confidence: 99%

A Low-order Nonconforming Finite Element for Reissner--Mindlin Plates

Lovadina

2005

SIAM J. Numer. Anal.

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“…A number of lockingfree individual finite elements and finite element families (e.g. [5,10,15,18,19,16,20,17]) have been obtained in this way.…”

Section: Introductionmentioning

confidence: 99%

Locking-free Reissner–Mindlin elements without reduced integration

Arnold

Brezzi

Falk

et al. 2007

Computer Methods in Applied Mechanics and Engineering

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In a recent paper of Arnold et al. [D.N. Arnold, F. Brezzi, L.D. Marini, A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate, J. Sci. Comput. 22 (2005) 25-45], the ideas of discontinuous Galerkin methods were used to obtain and analyze two new families of locking free finite element methods for the approximation of the Reissner-Mindlin plate problem. By following their basic approach, but making different choices of finite element spaces, we develop and analyze other families of locking free finite elements that eliminate the need for the introduction of a reduction operator, which has been a central feature of many locking-free methods. For k P 2, all the methods use piecewise polynomials of degree k to approximate the transverse displacement and (possibly subsets) of piecewise polynomials of degree k À 1 to approximate both the rotation and shear stress vectors. The approximation spaces for the rotation and the shear stress are always identical. The methods vary in the amount of interelement continuity required. In terms of smallest number of degrees of freedom, the simplest method approximates the transverse displacement with continuous, piecewise quadratics and both the rotation and shear stress with rotated linear Brezzi-Douglas-Marini elements.

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Locking-free finite elements for the Reissner-Mindlin plate

Cited by 44 publications

References 36 publications

A new MITC finite element method for Reissner--Mindlin plate problem based on a biorthogonal system

A new MITC finite element method for Reissner--Mindlin plate problem based on a biorthogonal system

A Low-order Nonconforming Finite Element for Reissner--Mindlin Plates

Locking-free Reissner–Mindlin elements without reduced integration

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